MORBID

Prof. Per Jensen's Fortran program for calculation of rovibrational energies for a triatomic molecule in an isolated electronic state

For details see and cite [Per Jensen, J. Molec. Spectrosc., 128, 478 (1988))[https://doi.org/10.1016/0022-2852(88)90164-6].

To compile

  gfortran -mcmodel=medium -o morbid *.f

To run:

  ./morbid <input > output 

Some examples of MORBID input files can be found in 'molecules'.

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Explanations:

The calculations are done for one J value at a time. The effects of the non-zero electron spin in non-singlet electronic states are neglected so in reality, J=N. Search for "ZERO POINT" to find

0************ ZERO POINT ENERGY ************

        E0 =   2711.21736

0************ J = 0 ENERGIES ************

to find the start of the energy tables (the zero point energy is given relative to the potential minimum) and for "J =" to find the start of the tables for subsequent J values.

For each J value, there is a column for each symmetry (A',A'') in the C_s(M) molecular symmetry group. The energies with a given J value and a given symmetry are labeled with the "non-good" quantum numbers:

KA V2 NS

These quantum numbers are obtained from the basis function with the largest contribution to the eigenfunction in question. KA is the usual $K_a$, V2 is $v_2$, the principal bending quantum number appropriate for a triatomic molecule with a bent equilibrium structure (see Section 17.5.2 of P.R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, NRC Research Press, Ottawa, 1998). The NS refers to the following table in the output file:

0 ************ A1 STRETCHING FUNCTIONS ************

     FCT. #        N1        N3            ENERGY/CM-1


          1         0         0              2565.89331
          2         0         1              3836.49142
          3         0         2              5090.10808
          4         1         0              6281.45001
          5         0         3              6326.91951
          6         0         4              7544.57681
          7         1         1              7554.14147
          8         0         5              8749.22967
          9         1         2              8806.09251
         10         2         0              9821.21858
         11         0         6              9935.75386
         12         1         3             10042.64425

FCT # = NS+1 (sorry about the +1). For a given NS value, the table now gives the N1, N3 values for the Morse oscillator product state with the largest contribution to the eigenfunction. The ordinary harmonic oscillator quantum numbers v1 and v3 can be obtained from N1+N3 = v1+v3.

The K_c quantum number can be obtained from symmetry analysis (see Chapter 12 of P.R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, NRC Research Press, Ottawa, 1998) in conjunction with the fact that K_a + K_c = J or J+1. I believe that K_c is even for A' symmetry and odd for A'' symmetry but that should be checked.